The sum of two numbers is $137$, and their difference is $5$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 137}$ ${x-y = 5}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 142 $ $ x = \dfrac{142}{2} $ ${x = 71}$ Now that you know ${x = 71}$ , plug it back into $ {x+y = 137}$ to find $y$ ${(71)}{ + y = 137}$ ${y = 66}$ You can also plug ${x = 71}$ into $ {x-y = 5}$ and get the same answer for $y$ ${(71)}{ - y = 5}$ ${y = 66}$ Therefore, the larger number is $71$, and the smaller number is $66$.